The Multiplier Ideals of a Sum of Ideals
Algebraic Geometry
2007-05-23 v2 Commutative Algebra
Abstract
Let X be a smooth variety and J, K two ideal sheaves on X. We prove the following formula relating the multiplier ideals of J, K and J+K: I(X, c(J+K))\subset \sum_{a+b=c} I(X, aJ)\cdot I(X,bK). An analogous formula holds for the asymptotic multiplier ideals of two graded systems of ideals. As a consequence, we show how to approximate at any given point arbitrary multiplier ideals by multiplier ideals of zero dimensional ideals. We apply this to study the invariance of multiplier ideals under different embeddings.
Keywords
Cite
@article{arxiv.math/0102217,
title = {The Multiplier Ideals of a Sum of Ideals},
author = {Mircea Mustata},
journal= {arXiv preprint arXiv:math/0102217},
year = {2007}
}
Comments
16 pages; LaTeX. Notational and expository changes, a mistake in the statement of Proposition 2.1 is corrected; to appear in Trans. Amer. Math.Soc